Geometry & Topology 1 (1997) 1–7

DOI: 10.2140/gt.1997.1.1

arXiv: math.GR/9702231

Abstract

We show that groups satisfying Kazhdan’s property (T) have no unbounded actions on finite dimensional CAT(0) cube complexes, and deduce that there is a locally CAT(−1) Riemannian manifold which is not homotopy equivalent to any finite dimensional, locally CAT(0) cube complex.

Keywords

Kazhdan's property (T), Tits' buildings, hyperbolic geometry, CAT(0) cube complexes, locally CAT(-1) spaces, Sp(n,1)–manifolds

Mathematical Subject Classification

Primary: 20F32

Secondary: 20E42, 20G20

References

Forward citations

Publication

Received: 28 October 1996
Accepted: 6 February 1997
Published: 7 February 1997
Proposed: Walter Neumann
Seconded: David Gabai, Robion Kirby

Authors